Various percussion instruments (marimbas, xylophones, and vibraphones) have a series of sound bars or keys that a player strikes with a mallet to obtain a desired musical melody or the notes of a composition. A marimba is a keyboard percussion instrument with a resonator tube below each key to enhance the sounds. The lengths of the resonator tubes adjacent the longer or lower-pitched keys must be correspondingly longer for in order to match the lower pitches of their respective adjacent keys. However if a marimba's keys are mounted at a playable height, say 75 cm (about 30 in), the longest or lowest-pitch resonator tubes must be very long—too long to clear the floor. This problem has been overcome by various techniques. One technique is to bend the bottom portions of the lowest-pitch tubes upwardly using U-shaped bends to keep keeping them away from the floor. Another technique is to extend the bottoms of the longer tubes into large box-shaped bottoms, thereby to increase their effective length by approximating a Helmholtz resonator. (The Helmholtz resonator is discussed infra.) A third technique is to mount a shorter, narrower auxiliary virtual-extender tube (VET) on the wall inside the main tube, near the top.
The following is a list of some prior art that illustrates these techniques for effectively extending the lengths of the longer resonator tubes:
Pat. or Pub. Nr.Kind CodeIssue or Pub. DatePatentee or Applicant  967,911B1Aug. 23, 1910Haskell1,128,112B1Feb. 9, 1915Deagan1,173,785B1Feb. 29, 1916Deagan1,207,281B1Dec. 5, 1916Deagan1,969,591B1Aug. 7, 1934Willis20080105105A1May 8, 2008Stevens
Haskell shows a bass or effective length or virtual extender tube (VET) A mounted inside a main organ tube B. Tube B has an adjustable tuning stopper E at its top and tube A is suspended from stopper E by two threaded rods F (Haskell, FIG. 5) that are attached to the outside of tube A. Thus when adjusting stopper E is moved, VET A moves with it. Instead of dangling freely from stopper E, the bottom end of VET A is springably urged against the inside of tube B. Haskell's organ pipes comprise open exterior tubes with closed interior extension tubes for lowering the resonant frequency of the pipe. The fundamental resonant frequency of a closed organ pipe is given by the formula f=(v/4L′)/4, where v is the speed of sound in air, and L′ is the length of the pipe. Placing a VET inside the organ pipe effectively increases the length of the pipe by an amount equal to the length of the extender tube, thereby lowering the resonant frequency of the pipe. This addition enables construction of organ pipes that are shorter than conventional organ pipes yet have the same fundamental resonant frequency.
In his patents, Deagan shows telescoping, interior resonating tubes or VETs for pianos and marimbas. His inner resonating tubes are adjustably secured within the main tubes by clamping screws ('112 patent) and clamping bars ('785 and '281 patents). In his '112 patent, Deagan's VET is partially conical and terminates in a thin diaphragm adjacent the vibrating body, i.e., tone bar, of the instrument. In his '785 and '281 patents, his interior resonating tube is partially conical and terminates in a thin diaphragm at the end of the tube opposite the vibrating body.
Haskell and Deagan's VETs are situated within the main resonating tube. Excitation of the air in the column is initiated at the entrance to the external tube.
Willis shows organ pipes with various tuning tubes that are slidably suspended from the sides of the main tubes by webs between the two tubes. Once the tubes are in the desired position, the webs can be secured to the pipes by solder.
Stevens shows a resonating tube for a percussion instrument. A tubular resonator is bent or formed into a smooth L-shaped, J-shaped, or U-shaped curve that is either open or stopped on one end.
Another tubular resonator is ascribed to physicist and physiologist Hermann von Helmholtz. In 1863, Helmholtz published a book, “On the Sensations of Tone as a Physiological Basis for the Theory of Music”. He describes a resonator, well known and understood today, that comprises an external necked region that is coupled on one end to a resonant cavity and on the other end to open air. Blowing across the neck of the resonator, or otherwise driving air into the resonator and then allowing the air to escape produces a tone whose fundamental frequency is given by the well-known Helmholtz equation fH=(v/2π)(A/VoL)1/2, where fH is the Helmholtz frequency, v is the speed of sound in air, A is the cross-sectional area of the neck, Vo is the volume of the cavity, and L is the length of the neck. An example is the tone generated by blowing across the neck of a soft drink bottle.
While all of the prior-art resonators are adaptable to percussion instruments, we found that they have one or more sound-quality drawbacks, including a weak fundamental frequency and distortion of the sounds created by the keys and their respective tubes.